The present invention relates to audio signal processing and, in particular, to an apparatus and a method for edge fading amplitude panning for 3D loudspeaker setups.
After the progression from stereo to 5.1 surround sound, the move towards 3D audio can be regarded as the next step in the evolution of movie and home cinema sound systems. A greater number of loudspeakers can extend the listening area and improve the spatial resolution of the reproduced sound field. However, a greater number of loudspeakers also means a greater demand, because more loudspeakers need to be placed where they are supposed to be. In a domestic environment like a living room it can be difficult to place them according to the specification. In practice, the placement and the number of involved loudspeakers is a compromise between sound quality, costs, aesthetics, spatial limitations, and also domestic/social aspects (see [20]).
Object-based audio scenes do not require a specific loudspeaker configuration like channel-based content and thus have less demands on the placement of the loudspeakers. The rendering process involves a panning method where the object's sound signal is played back by more than one loudspeaker (see [7]).
According to the known technology, for creating auditory events between the loudspeakers of a 3D speaker setup, Vector Base Amplitude Panning (VBAP) is a widely used method, which can be regarded as an extension to the tan-law (see [17], [5]). While this approach has proven its suitability for daily use, it is not ideal in all situations.
In the following VBAP is briefly described. VBAP uses a set of N unit vectors I1, . . . , IN which point at the loudspeakers of the 3D speaker set. A panning direction given by a Cartesian unit vector p is defined by a linear combination of those loudspeaker vectors according to formula (1):p=[l1, . . . ,lN][g1, . . . ,gN]T  (1)where gn denotes the scaling factor that is applied to In. In 3, a vector space is formed by 3 vector bases.
Formula (1) can generally be solved by a matrix inversion, if the number of active speakers and thus the number of non-zero scaling factors is limited to 3. Practically, this is done by defining a mesh of triangles between the loudspeakers and by choosing those triplets for the area in between. This leads to the solution[gn1,gn2,gn3]T=[ln1,ln2,ln3]−1p  (2)where {n1, n2, n3} denotes the active loudspeaker triplet.
Finally, a normalization that ensures power normalized output signals results in the final panning gains a1, . . . , aN:
                              a          n                =                              g            n                                                                          [                                                      g                    1                                    ,                  …                  ⁢                                                                          ,                                      g                    N                                                  ]                            T                                                                      (        3        )            VBAP exhibits particular properties. The vector arithmetic based concepts of VBAP are in relation to the sound field which is created by the involved loudspeakers. The base vector that corresponds to a certain loudspeaker, e.g., Gerzon's velocity vector (see [9]), coincides with the particle velocity that can be measured under free field conditions at the listener position. A linear combination of the sound fields created by two or more loudspeakers results in the linear combination of the particle velocity.
VBAP reproduces under free field conditions the particle velocity at the sweet spot that results from a sound source at the panning position.
As the human auditory system senses the sound pressure instead of the particle velocity (see [4]) and further involves directional filtering and cognitive processes, there is actually no direct relation between the underlying vector arithmetic and human localization.
However, sum localization works fairly well for small angles between horizontally arranged loudspeakers in the frontal or rear area [6]. For angles significantly larger than 90°, loudspeakers at the side, or vertically arranged loudspeaker positions, the sum localization is less convincing (see [21], [10], [15]).
FIG. 19 illustrates the VBAP panning gains for a common 5.1 surround setup (see [13]). Between the two rear speakers at 110° and 250°, rather flat curves and a low level difference for a wide angular range are observed. For an angular range where sum localization is not really working, VBAP results in even smaller level differences than for a smaller opening angle where sum localization is working. The reason for this behavior is the great opening angle between the vector bases.
In FIG. 20, a generalized VBAP method using an imaginary loudspeaker (light gray) and a downmix is depicted.
For a 3D loudspeaker setup, VBAP uses 3 base vectors depending on the chosen triangulation. If the 3D setup consists of two or more height layers stacked on top of each other with loudspeakers at the same azimuth angles, then there is no preference for a certain triangulation. For each section between two speakers of a layer, there are two possibilities for subdividing the rectangle between the middle and the upper layer speakers into two triangles. This arbitrary choice introduces an asymmetry even for perfectly symmetric setups. To illustrate this property, let us take a 5.1 setup as an example that has been extended by four height speakers above the M30, M-30, M110, and M-110 speakers i.e., U30, U-30, U110, and U-110 [14]. Between the middle and the upper layer surround speakers, the subdivision into the two triangles can either be defined by the diagonal M110↔U-110 or by the diagonal U110↔M-110. The same holds for the area above/between the upper layer loudspeakers. Whatever choice is made, it breaks the left-right symmetry. As a consequence, an audio object that moves from the upper front right to the upper rear left would sound different then if it would move from upper front left to upper rear right—despite the symmetry of the loudspeaker setup.